Square Root Calculator › Square root of 601
Square Root of 601
√601 ≈ 24.515301
601 is not a perfect square, so √601 is an irrational number that is approximately 24.515301. In simplified radical form, √601 = √601.
√601 lies between √576 = 24 and √625 = 25.
| Number | 601 |
| Square root (decimal) | 24.515301 |
| Simplified radical | √601 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 601
601 = 601. This is what determines the simplified radical: for √601 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √601 is already in simplest radical form as √601.
Estimating √601 by hand
√601 falls between √576 = 24 and √625 = 25, so it starts at 24.something. The Babylonian method refines that guess by averaging it with 601 ÷ the guess:
| Step | Estimate |
| Start | 24 |
| Step 1 | 24.520833 |
| Step 2 | 24.515302 |
| Step 3 | 24.515301 |
After 3 steps the estimate is 24.515301, matching √601 ≈ 24.515301.
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Frequently asked questions
Is 601 a perfect square?
No, 601 is not a perfect square, so its square root is irrational and approximately 24.515301.
What is the square root of 601 in simplest radical form?
√601 = √601 in simplest radical form.